PROBLEM

The backup fails with a Microsoft VSS Error, "A problem with Windows Shadow Copy was detected":

As the error suggests, if you take a look at the Hyper-V VMMS event log (Event Viewer → Application and Services Logs → Microsoft → Windows → Hyper-V-VMMS → Admin), you'll find the following event:

Source: Hyper-V VMMS | Event ID: 10178

Failed to fix-up absolute VHD paths in configuration of virtual machine 'Exchange': Account restrictions are preventing this user from signing in. For example: blank passwords aren't allowed, sign-in times are limited, or a policy restriction has been enforced. (0×8007052F). (Virtual machine ID E26C9A7B-8DDC-4775-AD85-13F2AACF51AF)

CAUSE

This issue occurs because the NT Virtual Machine\Virtual Machines special identity does not have the Log on as a Service right on the Hyper-V host computer and thereby VSS isn’t able to run successfully.